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Cellular automata simulation of topological effects on the dynamics of feed-forward motifs.

Apte AA, Cain JW, Bonchev DG, Fong SS - J Biol Eng (2008)

Bottom Line: Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production.It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner.These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Chemical and Life Science Engineering, Virginia Commonwealth University, P,O, Box 843028, Richmond, VA 23284, USA. ssfong@vcu.edu.

ABSTRACT

Background: Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems.

Results: Feed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production.

Conclusion: It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models.

No MeSH data available.


Related in: MedlinePlus

A scheme illustrating the rules that control the dynamics of the enzymatic reaction steps i. Here S, P, E, SE and PE stand for substrate, product, enzyme, substrate/enzyme and product/enzyme, respectively. The probability of motion is 1/k, k = 1 to 4 being the number of unoccupied neighboring cells; probability equal to 1 is postulated for S(i) and E(i) to join, as well as for PE(i) to disjoin. The transitional probability for the PE(i) formation is assumed equal to 0.5, which makes the first reaction step reversible.
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Figure 1: A scheme illustrating the rules that control the dynamics of the enzymatic reaction steps i. Here S, P, E, SE and PE stand for substrate, product, enzyme, substrate/enzyme and product/enzyme, respectively. The probability of motion is 1/k, k = 1 to 4 being the number of unoccupied neighboring cells; probability equal to 1 is postulated for S(i) and E(i) to join, as well as for PE(i) to disjoin. The transitional probability for the PE(i) formation is assumed equal to 0.5, which makes the first reaction step reversible.

Mentions: Cellular automata (CA) are modeling tools that represent dynamic systems discretely in space, time, and state. The overall system behavior is specified entirely by rules governing local relationships. In the most common 2D-version, CA models are constructed on a grid of squares called cells. The grid size may vary considerably, depending on the system. To eliminate any boundary effects, the grid is usually built on the surface of a torus. In our study we used lattices within the range of 100 × 100 to 220 × 220 (fide infra). The following rules were employed (See Fig. 1 for an illustration of the most essential probabilistic rules):


Cellular automata simulation of topological effects on the dynamics of feed-forward motifs.

Apte AA, Cain JW, Bonchev DG, Fong SS - J Biol Eng (2008)

A scheme illustrating the rules that control the dynamics of the enzymatic reaction steps i. Here S, P, E, SE and PE stand for substrate, product, enzyme, substrate/enzyme and product/enzyme, respectively. The probability of motion is 1/k, k = 1 to 4 being the number of unoccupied neighboring cells; probability equal to 1 is postulated for S(i) and E(i) to join, as well as for PE(i) to disjoin. The transitional probability for the PE(i) formation is assumed equal to 0.5, which makes the first reaction step reversible.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2278126&req=5

Figure 1: A scheme illustrating the rules that control the dynamics of the enzymatic reaction steps i. Here S, P, E, SE and PE stand for substrate, product, enzyme, substrate/enzyme and product/enzyme, respectively. The probability of motion is 1/k, k = 1 to 4 being the number of unoccupied neighboring cells; probability equal to 1 is postulated for S(i) and E(i) to join, as well as for PE(i) to disjoin. The transitional probability for the PE(i) formation is assumed equal to 0.5, which makes the first reaction step reversible.
Mentions: Cellular automata (CA) are modeling tools that represent dynamic systems discretely in space, time, and state. The overall system behavior is specified entirely by rules governing local relationships. In the most common 2D-version, CA models are constructed on a grid of squares called cells. The grid size may vary considerably, depending on the system. To eliminate any boundary effects, the grid is usually built on the surface of a torus. In our study we used lattices within the range of 100 × 100 to 220 × 220 (fide infra). The following rules were employed (See Fig. 1 for an illustration of the most essential probabilistic rules):

Bottom Line: Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production.It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner.These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Chemical and Life Science Engineering, Virginia Commonwealth University, P,O, Box 843028, Richmond, VA 23284, USA. ssfong@vcu.edu.

ABSTRACT

Background: Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems.

Results: Feed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production.

Conclusion: It was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models.

No MeSH data available.


Related in: MedlinePlus